What causes this bug, and how can I avoid it? I'm using the building tools plugin, and usually draw the seperate parts of the building with one of the marked so it follows the same angle. From what I have collected, it might have to do with some node going a bit out of the completed polygon, if that makes sense. The bug seems crazy anyway though...

I think the JOSM "combine" feature works fine only when polygons are strictly adjacent, mean not overlapping or nodes not joined to the nearest way. More than a screenshot, your bug report should provide an XML file ('save as' in JOSM) of the building blocks you want to combine (e.g. copy them to a new layout and save). This will be used as a test dataset for the developers.